@lakens Your discussion of #pvalues is really a bit odd. "Just calculate a number that has no real interpretation, and then interpret it cautiously."* That's bogus.
Importantly, you missed the opportunity to making the point that, relatively, your p-values do have an interpretation: If you order your effects by p-value from low to high, the top of this list contains better candidates for a future study than the bottom.
*these are my words paraphrasing/interpreting Daniel Lakens
@lakens third: Although I missed your point, the gist of what I say is still a valid critique, I believe:
You write the line mentioned above as a sidenote explaining why "testing" is not warranted.* I think this is the only thing for which a p-value (or whatever monotonic test statistic) is useful in an exploratory analysis.
*by the way: you don't mention that the p-value has no absolute interpretation here, which I think is quite crucial. For that, your "not warranted" is not clear enough
@lakens So, I would shorten your section "exploratory testing" to: "Exploratory testing is a contradiction. You can, however, calculate a p-value to order your observed effects by probability of representing a true effect."
Could you agree with that?
Gilles DePemig 
Daniel Lakens